Laser cutting is assisted by adding gas. Oxygen, nitrogen, argon or air are used as cutting gases. Different gases are used depending on laser processing. When changing gases, the previously used gas must preferably be completely expelled or escape, and be replaced by another gas, since residual gas amounts of the previously used gas may have a detrimental effect on subsequent laser processing. Known flushing methods include evacuating the nozzle of a laser processing head before changing gases, or extending the continuous flushing time until any foreign gas has been removed from the process gas. Only a little flow forms in individual areas of the gas path between the gas valve and the cutting nozzle when the gas is flowing at a constant rate, such that it is not possible to quickly expel all of the previously used gas. While insufficient flushing times reduce the process quality, excessive flushing times reduce the productivity or incur unnecessary costs through gas consumption.